Cameron Norrie clinched his first win against a world top-10 opponent to knock John Isner out of the Lyon Open.
Norrie, 22, saved all four break points he faced against big-serving Isner, who the Briton broke for the only time in the first game of the second set before sealing victory in 85 minutes.
Simon hit back from a set down to beat Kazakhstan's Mikhail Kukushkin 4-6 6-4 7-6 (7/5).
Serbia's Dusan Lajovic overcame American Taylor Fritz 7-5 6-1 in the other quarter-final and will play Dominic Thiem or Guillermo Garcia-Lopez.
Top-seeded Austrian Thiem was locked at one set all with Spain's Garcia-Lopez before play was suspended due to bad light.
At the Geneva Open, Hungary's Marton Fucsovics upset defending champion Stan Wawrinka 6-4 6-0 to reach the last four.
Wawrinka, back on the circuit after two operations on his left knee, failed to convert seven of his eight break points against Fucsovics and crashed out in 75 minutes.
Fucsovics will next face American Steve Johnson, who beat Guido Pella 6-3 6-4 in his second match of the day, having earlier won through to the last eight with a 6-4 4-6 6-3 win against Lukas Rosol.
Italy's Fabio Fognini celebrated his 31st birthday with a 7-6 (7/3) 7-6 (7/5) victory over American Tennys Sandgren to set up a last-four clash with German Peter Gojowczyk, who overcame Andreas Seppi 6-3 6-7 (3/7) 6-3.